If two solutions Y less than or equal to Z of the DARE are given then the s
et of solutions X with Y less than or equal to X less than or equal to Z ca
n be parametrized by invariant subspaces of the closed loop matrix correspo
nding to Y. The paper extends the geometric theory of Willems from the cont
inuous-time to the discrete-time ARE making the weakest possible assumption
s. (C) 1999 Elsevier Science B.V. All rights reserved.